About 48% of them do. In other words, the males do, the females don't.

To be absolutely correct, please note that, though testicles refers to
testes in general which are present in all male mammals, the term testicles
is especially used for those contained within a scrotum (the normal
condition of mammals). Whales (and some pinnipeds) are the exception. The
testes are contained within the body -- no external scrotum.

So, technically sperm whales do have testicles held inside the body, but it
is more correct to say they have testes (testis singular).

One should also note that for the sperm whale, its name does not derive
from impressive testicles. The name comes from the similar consistency of
the oil in the head of the whale (spermaceti organ) and sperm. The
impressive testicle award (high volume) apparently goes to the bowhead
whale.

Note: visit Discovery Online (US version) and go to the Madagascar humpback
whale page. There you will see some of my work, including an animated clip
on feeding humpbacks.